Relation 1 is a function because any input item in the domain leads to exactly one and only one output item in the range. If we had say 2 arrows coming from "chair", and pointing to two different outputs, then we wouldn't have a function. It's perfectly possible to use words in place of numbers when talking about functions. All that matters is that we have one input map to exactly one output.
Relation 2 is a function for similar reasoning as relation 1. It's possible to have an output repeated and still have a function.
Relation 3 is not a function. Why not? Because of the points (j,v) and (j,t). The input j leads to more than output (v and t at the same time). A similar issue happens with the input 's' also.
Relation 4 is also not a function. The repeated input this time is -5 which maps to the outputs z and 'a' at the same time.
